Math / Data & Statistics

QuestionPYC ALEKS A ALEKs - Keyah Jackson - Learn FSC Grades for Keyah Jackson: Fall-2248-ISM401 Confidence Intervals and Hypothesis Testing Introduction to the chi-square distribution
A chi-square distribution with 8 degrees of freedom is graphed below. The region under the curve to the right of 6 is shaded.
Find the area of the shaded region. Round your answer to three decimal places. $\square$ Explanation Check

Studdy Solution

STEP 1

1. We are dealing with a chi-square distribution with 8 degrees of freedom.
2. The task is to find the area to the right of 6 under this chi-square distribution curve.
3. The area under the curve represents probabilities, and we will use statistical tables or software to find this area.
4. The result should be rounded to three decimal places.

STEP 2

1. Understand the chi-square distribution and degrees of freedom.
2. Use a chi-square distribution table or software to find the cumulative probability up to 6.
3. Calculate the area to the right of 6 by subtracting the cumulative probability from 1.

STEP 3

Understand that a chi-square distribution is a continuous probability distribution that is skewed to the right, and it is defined by its degrees of freedom. In this case, we have 8 degrees of freedom.

STEP 4

Use a chi-square distribution table or statistical software to find the cumulative probability $P(X \leq 6)$ for a chi-square distribution with 8 degrees of freedom.

STEP 5

Using a chi-square table or software, find $P(X \leq 6)$ . For 8 degrees of freedom, this cumulative probability is approximately 0.3446.

STEP 6

Calculate the area to the right of 6, which is $1 - P(X \leq 6)$ .
$1 - 0.3446 = 0.6554$
Round the result to three decimal places:
$\boxed{0.655}$
The area of the shaded region is:
$\boxed{0.655}$

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Studdy Solution

STEP 1

STEP 2

1. Understand the chi-square distribution and degrees of freedom.
2. Use a chi-square distribution table or software to find the cumulative probability up to 6.
3. Calculate the area to the right of 6 by subtracting the cumulative probability from 1.

STEP 3

Understand that a chi-square distribution is a continuous probability distribution that is skewed to the right, and it is defined by its degrees of freedom. In this case, we have 8 degrees of freedom.

STEP 4

Use a chi-square distribution table or statistical software to find the cumulative probability $P(X \leq 6)$ for a chi-square distribution with 8 degrees of freedom.

STEP 5

Using a chi-square table or software, find $P(X \leq 6)$ . For 8 degrees of freedom, this cumulative probability is approximately 0.3446.

STEP 6

Calculate the area to the right of 6, which is $1 - P(X \leq 6)$ .
$1 - 0.3446 = 0.6554$
Round the result to three decimal places:
$\boxed{0.655}$
The area of the shaded region is:
$\boxed{0.655}$

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Studdy Solution

STEP 1

STEP 2

1. Understand the chi-square distribution and degrees of freedom.2. Use a chi-square distribution table or software to find the cumulative probability up to 6.3. Calculate the area to the right of 6 by subtracting the cumulative probability from 1.

STEP 3

Understand that a chi-square distribution is a continuous probability distribution that is skewed to the right, and it is defined by its degrees of freedom. In this case, we have 8 degrees of freedom.

STEP 4

Use a chi-square distribution table or statistical software to find the cumulative probability P(X≤6) P(X \leq 6) P(X≤6) for a chi-square distribution with 8 degrees of freedom.

STEP 5

Using a chi-square table or software, find P(X≤6) P(X \leq 6) P(X≤6). For 8 degrees of freedom, this cumulative probability is approximately 0.3446.

STEP 6

Calculate the area to the right of 6, which is 1−P(X≤6) 1 - P(X \leq 6) 1−P(X≤6).1−0.3446=0.6554 1 - 0.3446 = 0.6554 1−0.3446=0.6554Round the result to three decimal places:0.655 \boxed{0.655} 0.655​ The area of the shaded region is:0.655 \boxed{0.655} 0.655​

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Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

1. Understand the chi-square distribution and degrees of freedom.
2. Use a chi-square distribution table or software to find the cumulative probability up to 6.
3. Calculate the area to the right of 6 by subtracting the cumulative probability from 1.

Use a chi-square distribution table or statistical software to find the cumulative probability $P(X \leq 6)$ for a chi-square distribution with 8 degrees of freedom.

Using a chi-square table or software, find $P(X \leq 6)$ . For 8 degrees of freedom, this cumulative probability is approximately 0.3446.

Calculate the area to the right of 6, which is $1 - P(X \leq 6)$ .
$1 - 0.3446 = 0.6554$
Round the result to three decimal places:
$\boxed{0.655}$
The area of the shaded region is:
$\boxed{0.655}$